A visa can be issued 365 days ahead, but you can only enter 30 days early
For new students an F or M visa can be issued up to 365 days before the start date on the I-20 (the old limit was 120), but entry is allowed no earlier than 30 days before that date.
You can start as soon as the I-20 arrives, in this order: I-20, SEVIS I-901, DS-160, visa fee, appointment, AIT interview. The official advice is at least three months before you plan to leave Taiwan. If you would arrive after the date on the I-20, no visa is issued until the school changes that date in SEVIS. The 365-day and 30-day limits apply to new students only; continuing students in status with a current SEVIS record can reapply and re-enter at any time. After arrival, check the I-94: the period of stay runs off it, not the I-20.
Can my spouse or children come with me?
Yes, on an F-2 visa. The school issues a separate I-20 for each dependent, and the interview needs English proof of the relationship (marriage certificate, household registration and so on). F-2 holders cannot work in the US, and do not pay the SEVIS fee.